# Tag Archives: enumeration

## Up or Right

Starting at the point on the coordinate plane, a pin can be moved either to point or to point . If the pin starts at and is moved to , what is the probability that it passed through ? Source: … Continue reading

## Sum of 1/i

Find the sum of where . Source: NCTM Mathematics Teacher, February 2006 SOLUTION Multiply both sides by The above expression hasĀ terms with the middle term equal We combine the first term to the last term, the second to the … Continue reading

## Socks of Same Color

Sean has a drawer containing black socks, brown socks, blue socks, and green socks, all loose and not properly paired. Sean takes socks out of the drawer at random without replacement, in the dark. How many socks must Sean take … Continue reading

## Cutting Pizza

What is the largest number of pieces into which a circular pizza can be cut with straight cuts? Source: NCTM Mathematics Teacher 2006 SOLUTION Please refer to post “Regions in the Plane” posted 1/5/2012. Answer:

## 10 Digit Call

A typical telephone number in the United States used to be digits. While you can still use a seven-digit code in most areas, a multitude of regions have begun using ten-digit telephone numbers. If the entire country goes to a … Continue reading

## 23569 Sum

Using the five digits , and , what is the sum of all positive three-digit integers using these five digits? Please note that the same digit can appear more than once. Source: mathcontest.olemiss.edu 4/15/2013 SOLUTION This problem is similar to … Continue reading

## 23567

Find the sum of all positive three-digit integers formed from the five digits: , and . The same digit can appear more than once. Source: mathcontest.olemiss.edu 3/4/2013 SOLUTION Let’s try a smaller problem to get an idea of what’s going … Continue reading

## Diagonals in Octagons

How many more diagonals are in an octagon than in a hexagon? Source: NCCTM Mathematics Teacher SOLUTION We draw a diagonal by connecting two non-adjacent vertices. For example, is a diagonal but and are not. How many ways can we … Continue reading

## Red or Blue Cube

A cube’s faces are colored either red or blue. Each occurrence has a probability of . The color of each face is determined independently. If the painted cube is placed on a horizontal surface, what is the probability of vertical … Continue reading

## Matching Socks and Shoes

1. I have ten black and ten brown socks loose in a drawer. In the dark, what is the least number of socks I must pull out to ensure myself that I have a matching pair? 2. In my closet … Continue reading